Precision calculation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>N</mml:mi> <mml:mi>eff</mml:mi> </mml:msub> </mml:math> with neutrino direct simulation Monte Carlo

Neutrino direct simulation Monte Carlo ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>ν</a:mi> <a:mi>DSMC</a:mi> </a:math> ) is a Monte Carlo method for solving the neutrino Boltzmann equation in the early Universe, designed to track the evolution of cosmic neutrinos across a wide range of cosmological scenarios. We develop a complete <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>ν</c:mi> <c:mi>DSMC</c:mi> </c:math> solver that consistently incorporates the effects of the electron mass, three-flavor neutrino oscillations, and finite-temperature QED corrections to the thermodynamics of the electromagnetic plasma. As a first application, we perform a high-precision calculation of neutrino decoupling in the standard cosmological model and obtain <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msub> <e:mi>N</e:mi> <e:mi>eff</e:mi> </e:msub> <e:mo>=</e:mo> <e:mn>3.0439</e:mn> <e:mo>±</e:mo> <e:mn>0.0006</e:mn> </e:math> , in excellent agreement with state-of-the-art results.